Large-span arch bridge bending moment active amplitude modulation method based on cable force in construction process

Abstract

The invention discloses a construction process cable force-based large-span arch bridge bending moment active amplitude modulation method, which relates to the technical field of bridge engineering, and comprises the following steps: establishing a large-span arch bridge space bar system unit model according to design parameters; calculating arch ring arch crown internal force according to the large-span arch bridge space bar system unit model; calculating a corresponding compression amount change value according to the internal force of the arch crown of the arch ring; the final amplitude modulation closure gap length is obtained according to the compression amount change value; and calculating the cable force of the large-span arch bridge according to the amplitude-modulated closure gap length, thereby realizing the amplitude modulation of the finished bridge bending moment of the large-span arch bridge. The bridge forming bending moment can be effectively reduced, and the structural safety is improved.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, and more specifically to a method for active adjustment of bending moment of a long-span arch bridge based on cable forces during construction. Background Technology

[0002] Long-span arch bridges are widely used in transportation engineering projects in complex terrains such as rivers and canyons due to their strong spanning capacity and excellent structural economy. Theoretically, a long-span arch bridge with a reasonable arch axis can achieve a zero bending moment state under dead load. However, in actual engineering, the arch ring is subject to elastic compression under dead load, overall temperature changes, concrete shrinkage and creep, and moving loads, which can easily generate additional internal forces, leading to peak bending stresses at the arch foot and crown. Long-term use can easily cause structural cracking and deterioration of load-bearing performance.

[0003] Existing technologies for adjusting the bending moment of completed bridges have significant limitations: First, traditional axial compression compensation methods often only consider the dead load effect, failing to systematically incorporate the coupled effects of temperature, shrinkage, and creep, and lack linkage with the construction process. The total internal force after adjustment may still exceed the control threshold. Second, while the influence matrix method can establish the relationship between closure parameters and internal forces, it does not form a closed-loop calculation system of "cable tension - closure state - completed bridge internal forces," resulting in low precision in on-site cable tension control and a tendency for the structural stress after closure to deviate from the design target. Third, existing methods often fail to iteratively correct the creep effect of concrete arch bridges. Excessive closure compensation lengths can easily lead to excessive compressive stress in the arch ribs under maximum cantilever conditions and concrete cracking, affecting construction safety.

[0004] With the breakthrough of long-span arch bridges reaching spans of 400-1000m, traditional amplitude adjustment techniques are no longer sufficient to meet the dual requirements of structural safety and construction control. Therefore, there is an urgent need for an active amplitude adjustment technology for the completed bridge bending moment that can combine precise control of cable forces during construction and take into account the coupled effects of multiple effects, in order to solve the problems of incomplete amplitude adjustment, poor construction adaptability, and insufficient long-term stability of existing methods.

[0005] According to the principle of minimum potential energy, the length of the closure joint... dx and corner ry The internal force state of the completed bridge after cable removal and closure has a unique mapping criterion, which can be adjusted by changing the length of the closure joint. dx and corner ry Adjusting the bending moment state of the long-span arch bridge upon completion. Simultaneously, considering the length of the closure section. dx and corner ry This can be achieved through cable force during construction, thus proposing a method for active moment adjustment of long-span arch bridges based on cable force during construction. Summary of the Invention

[0006] In view of this, the present invention provides a method for active adjustment of bending moment of long-span arch bridges based on cable forces during construction. To achieve the above objectives, the present invention adopts the following technical solution: a method for active moment adjustment of long-span arch bridges based on cable forces during construction, comprising: Establish a spatial frame unit model of the long-span arch bridge based on the design parameters; Calculate the internal forces at the crown of the arch ring based on the spatial frame element model of a long-span arch bridge; Calculate the corresponding change in compression based on the internal forces at the top of the arch ring; The final amplitude modulation closure length is obtained based on the change in compression. The cable force of the long-span arch bridge is calculated based on the length of the closure gap, thereby realizing the adjustment of the internal force of the completed long-span arch bridge.

[0007] Preferably, the design parameters include the span, rise, column spacing, material properties, and cross-sectional shape of the long-span arch bridge; the spatial truss unit model of the long-span arch bridge uses variable cross-section beam units to simulate the main arch, truss units to simulate the cable tie, beam units and truss units are connected at common nodes, and fixed boundary conditions are set at the arch foot and cable tie ends.

[0008] Preferably, the internal forces at the crown of the arch ring include Ms , Mg and Mc , Ms , Mg and Mc These represent the internal force values ​​for dead load, shrinkage, and creep calculated using the finite element method, respectively, with the values ​​at the top of the arch used for the calculation.

[0009] Preferably, the process of calculating the corresponding compression change value based on the internal force of the arch ring crown includes: compressive strain caused by constant load change, compressive strain caused by temperature change, compressive strain caused by shrinkage change, and compressive strain caused by creep. The compressive strain induced by dead load yields different expressions for dead load strain depending on the cross-sectional shape. ; Integrating the above equation, we obtain the expression for constant load compressive strain. ; in, Represents the compressive strain function under constant load. This represents the compression function of the arch rib under constant load. This represents the compressive strain value of the arch crown. a Indicates the curvature of the vault. l It represents half the arch span. A x This is a function representing the variation of the arch rib cross section. A 0 represents the cross-sectional area of ​​the arch crown. Indicates the horizontal inclination angle of the arch axis; The compressive strain caused by temperature change is expressed as ; in, This is the difference between the temperature at the time of closure and the average temperature. The coefficient of thermal expansion of the material. l It is represented as half the arch span. The compressive strain caused by contraction is calculated using the finite element method, as shown in the following formula: ; The compressive strain caused by creep is calculated based on the ratio of shrinkage to the bending moment of the dead load arch rib, using the following formula: .

[0010] The preferred expression for the final amplitude modulation closure gap length is as follows: dx =Δ lg +Δ lt +Δ ls +Δ lc。

[0011] Preferably, when the length of the closure joint changes, the stress state of the structure changes. At this time, the axial compression caused by constant load, overall temperature change, and shrinkage remains unchanged, while the axial compression caused by creep changes. Therefore, it is necessary to recalculate the ten-year creep internal force of the structure after the change in the closure joint length. M c With total internal force M i ; when M i / M g When <0.1, output the amplitude modulation closure gap length value at this time. dx .

[0012] Preferably, when there is no analytical expression for the cross-sectional area of ​​the compressive strain caused by the constant load, and the change in compression cannot be accurately calculated analytically, the influence matrix method is used to adjust the bending moment amplitude.

[0013] Preferably, the specific steps for bending moment amplitude adjustment using the influence matrix method include: Establish the arch crown bending moment after cable removal and arch construction Arch foot bending moment Length of the closure opening of the arch before the cable-stayed arch is dismantled With corner Relationship; ; For the influence matrix, These are the bending moments at the crown and abutments of the arch after the cables are removed and the arch is constructed; among which Represented as: ; These represent the arch crown bending moment values ​​after the cables are removed and the arch is formed by setting a unit horizontal displacement and rotation angle at the closure joint, respectively. These represent the arch foot bending moment values ​​after the cables are removed and the arch is formed by setting a unit horizontal displacement and rotation angle at the closure point, respectively. The coefficient matrix is ​​calculated using the finite element method. according to The coefficient matrix is ​​used to calculate the horizontal displacement dx and the rotation target ry at the closure point; .

[0014] Preferably, when the horizontal displacement of the closure joint changes, the total internal force M of the arch crown and arch foot of the structure after the change must be recalculated. i and M j ; If M i / M g <0.1 indicates that the internal forces of the completed bridge after adopting the active moment adjustment method for long-span arch bridges are less than one order of magnitude less than the capacity of a single bridge closure. Output the horizontal displacement of the current closure section. dx and corner ry .

[0015] Preferably, when the horizontal displacement of the closure joint... dx and corner target ry Once determined, the cable forces during construction must be calculated. T i ; Using the aforementioned spatial frame element model of the long-span arch bridge, the cable forces during construction were calculated. T i Horizontal displacement relative to the closure point dx and corner ry Influence Matrix D In the formula: T i Indicates the first i The initial tension of the horn cable;

[0016] Since the number of cable forces during construction must exceed 2, the two objectives of horizontal displacement and rotation at the closure point are insufficient to constrain the cable forces during construction. To further solve the problem, multiple optimization objectives such as cable force uniformity during construction and tower deflection during construction are introduced. This transforms the rankless matrix optimization problem into a linear equation problem, and the cable forces during construction are obtained from the solution.

[0017] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for active adjustment of bending moment of long-span arch bridges based on cable force during construction, with the following beneficial effects: 1. It can simultaneously compensate for the coupling effects of dead load, temperature, shrinkage and creep, reducing the total internal force of the completed bridge by an order of magnitude compared with the original dead load internal force (Mi / Mg<0.1), making the arch rib bending stress close to zero and the axial compressive stress uniform, greatly reducing the risk of structural cracking and significantly improving the long-term load-bearing safety of long-span arch bridges.

[0018] 2. By establishing a closed-loop calculation of "cable force - closure parameters - internal forces of completed bridge" through the influence matrix method, the cable force solution has high accuracy. With real-time monitoring and iterative correction, the excessive compressive stress of the arch rib under the maximum cantilever condition can be avoided, which is especially suitable for the safety requirements of concrete arch bridge construction.

[0019] 3. Applicable to various types of large-span arch bridges, such as steel arch bridges and concrete arch bridges with spans of 200-1000m, without requiring significant modifications to the structural design, and can be directly integrated with existing construction techniques, demonstrating outstanding practicality and compatibility.

[0020] 4. Reduce redundant material design caused by excessive internal forces, reduce construction rework rate, indirectly shorten construction period, and provide a low-cost and high-efficiency internal force optimization solution for the construction of large-span arch bridges under complex working conditions. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0022] Figure 1 The method flowchart provided by the present invention.

[0023] Figure 2 The axial compression diagram of the main arch provided by this invention.

[0024] Figure 3 The flowchart of the constant load and long-term effect bending moment amplitude adjustment method based on axial compression compensation provided by the present invention is shown.

[0025] Figure 4 The flowchart of the constant load and long-term effect bending moment amplitude adjustment method based on the influence matrix provided by the present invention is shown.

[0026] Figure 5 The bending moment diagram of the arch ring under full live load provided by this invention.

[0027] Figure 6 The stress diagram of the arch ring under full live load provided by this invention.

[0028] Figure 7 A comparison diagram of the dead load bending moment after the main arch is lowered and adjusted, provided for this invention.

[0029] Figure 8 The diagram shows the calculation parameters for the arch provided in this invention.

[0030] Figure 9 A comparison diagram of the bending moment after the main arch is lowered and adjusted, provided by this invention.

[0031] Figure 10 A comparison diagram of the bending moment of the lower arch rib with different closure opening lengths provided by the present invention.

[0032] Figure 11 The bending stress and bending moment diagrams before and after amplitude adjustment are provided for this invention.

[0033] Figure 12 The finite element model diagram of the arch bridge provided by this invention considers the construction stage.

[0034] Figure 13 The diagram shows the structural calculation results after the internal force amplitude is adjusted and the cables are removed to form an arch, as provided by this invention. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] like Figure 1 As shown, this invention discloses an active moment adjustment method for long-span arch bridges based on cable forces during construction, comprising: Establish a spatial frame unit model of the long-span arch bridge based on the design parameters; Calculate the internal forces at the crown of the arch ring based on the spatial frame element model of a long-span arch bridge; Calculate the corresponding change in compression based on the internal forces at the top of the arch ring; The final amplitude modulation closure length is obtained based on the change in compression. The cable force of the long-span arch bridge is calculated based on the length of the closure gap, thereby realizing the adjustment of the internal force of the completed long-span arch bridge.

[0037] Preferably, the design parameters include the span, rise, column spacing, material properties, and cross-sectional shape of the long-span arch bridge; the spatial truss unit model of the long-span arch bridge uses variable cross-section beam units to simulate the main arch, truss units to simulate the cable tie, beam units and truss units are connected at common nodes, and fixed boundary conditions are set at the arch foot and cable tie ends.

[0038] Preferably, the internal forces at the crown of the arch ring include Ms , Mg and Mc , Ms , Mg and Mc These represent the internal force values ​​for dead load, shrinkage, and creep calculated using the finite element method, respectively, with the values ​​at the top of the arch used for the calculation.

[0039] Preferably, the process of calculating the corresponding compression change value based on the internal force of the arch ring crown includes: compressive strain caused by constant load change, compressive strain caused by temperature change, compressive strain caused by shrinkage change, and compressive strain caused by creep. The compressive strain induced by dead load yields different expressions for dead load strain depending on the cross-sectional shape. ; Integrating the above equation, we obtain the expression for constant load compressive strain. ; Among them, among them, Represents the compressive strain function under constant load. This represents the compression function of the arch rib under constant load. The value represents the compressive strain at the crown, 'a' represents the curvature of the crown, and 'l' represents half the span of the arch. A x This is a function representing the variation of the arch rib cross section. A 0 The cross-sectional area of ​​the arch is... Indicates the horizontal inclination angle of the arch axis; The compressive strain caused by temperature change is expressed as ; in, This is the difference between the temperature at the time of closure and the average temperature. The coefficient of thermal expansion of the material. l It is represented as half the arch span. The compressive strain caused by contraction is calculated using the finite element method, as shown in the following formula: ; The compressive strain caused by creep is calculated based on the ratio of shrinkage to the bending moment of the dead load arch rib, using the following formula: .

[0040] Specifically, the final expression for the amplitude modulation closure gap length is as follows: dx =Δ lg +Δ lt +Δ ls +Δlc。

[0041] Specifically, when the length of the closure joint changes, the stress state of the structure changes. At this time, the axial compression caused by constant load, overall temperature change, and shrinkage remains unchanged, while the axial compression caused by creep changes. Therefore, it is necessary to recalculate the ten-year creep internal force M of the structure after the change in the closure joint length. c With total internal force M i ; When Mi / Mg < 0.1, the output value is the amplitude modulation closure length. dx .

[0042] In a specific embodiment of the present invention, a large-span arch bridge with a reasonable arch axis can theoretically achieve a zero-bending-moment state for a rigid arch structure under dead load. However, in reality, the arch ring will deform under dead load, overall temperature change, shrinkage and creep, and moving load, thereby causing internal forces in the main arch. Dead load, overall temperature change, and shrinkage and creep are all structural internal forces generated in the form of axial compressive deformation, which can be adjusted by compensating for the axial compression. The structural internal forces generated by moving loads are variable, and their distribution is inconsistent with the structural internal force effects generated by axial compressive deformation. Therefore, it is impossible to completely eliminate the structural internal forces generated by moving loads solely through compensation for axial compression. However, by adjusting the length and rotation angle of the arch crown closure section, the peak bending stress at each control section of the arch rib under a specific live load distribution mode can be made equal.

[0043] Furthermore, the method for adjusting the bending moment amplitude under dead load and long-term effects based on axial compression compensation includes: For long-span arch bridges with a reasonable arch axis, the bending moment of the arch rib caused by dead load, overall temperature change, shrinkage and creep is only generated by elastic compression. The internal forces generated by elastic compression, overall temperature change, shrinkage and creep can be eliminated by compensating for elastic compression, thereby achieving the purpose of adjusting the bending moment of the completed bridge.

[0044] Under constant load, overall temperature change, and shrinkage / creep, the elastic compression of the arch ring manifests as a shortening of the arch axis length. This deformation of the arch ring generates corresponding internal forces within the arch, resulting in maximum bending stress at the arch foot and crown. Taking a cantilevered curved beam as the basic structure, such as... Figure 2 As shown, elastic compression will shorten the arch axis in the span direction. ( (The elastic compression is the strain that causes the arch axis to shorten in the span direction). The elastic compression amount can be obtained by integrating the axial compression strain along the axis, as shown in equation (1).

[0045] (1)

[0046] If the length and angle of the closure joint are controlled to be 0 at this point, the structure is in a stress-free closure state, and the internal forces included in the construction process are the same as those in the first frame lowering. If axial compression compensation is performed at the closure joint, the internal forces generated by axial compression can be eliminated, making the bending moment after the arch is formed zero.

[0047] The axial compressive strain of the arch satisfies ,in Let represent the compressive strain caused by dead load, temperature, shrinkage, and creep, respectively. Among them, the compressive strain caused by dead load can be expressed in different ways according to different cross-sectional changes (2). Integrating equation (3), we can obtain the expression for the elastic compressibility under dead load (4).

[0048] (2); (3); The compressive strain caused by temperature change can be expressed as: .in, This is the difference between the temperature at the time of closure and the average temperature. Let be the coefficient of thermal expansion of the material. The axial compression caused by temperature change can be expressed as equation (4). (4) The compressive strain caused by shrinkage can be calculated according to Appendix C of the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG 3362-2018), or it can be calculated using the finite element method. Since the bending moment effects of shrinkage and dead load are distributed in the same way and have a proportional relationship, when using the finite element method, the axial compression caused by shrinkage can be calculated according to the ratio of the bending moment of the arch rib under shrinkage and the dead load, as shown in equation (5).

[0049] In equation (5), , These represent the dead load and shrinkage internal force values ​​calculated using the finite element method, respectively. The values ​​from the arch crown can be used for calculation. During the maximum cantilever stage, the arch and the stern must satisfy... , This allows for axial compression compensation under constant load, temperature, and shrinkage.

[0050] (5)

[0051] The compressive strain caused by creep is related to the structural stress. The axial compression compensated during the closure stage will change the structural stress, thereby affecting the creep process of the structure. Therefore, it is necessary to use finite element method to iterate multiple times to adjust the creep internal force. Similar to the shrinkage effect, the compressive strain caused by creep can be calculated according to the specifications and finite element method. When using finite element method, the axial compression caused by creep can be calculated according to the ratio of shrinkage to the bending moment of the dead load arch rib, as shown in equation (6).

[0052] (6)

[0053] In another specific embodiment of the present invention, in summary, the dead load and long-term effect bending moment adjustment method based on axial compression compensation proposed in this embodiment, as follows: Figure 3 As shown, the specific process is as follows: (1) Establish a spatial frame element model of the long-span arch bridge based on the design parameters; (2) Calculate the internal forces M in the arch ring and crown caused by dead load, shrinkage, and creep. g M s M c ; (3) Solve for Δlg, Δlt, Δls, and Δlc according to equations (4) to (6); (4) Set dx=Δlg+Δlt+Δls+Δlc at the closure point. In the finite element model, the temperature load of the beam element can be applied. The temperature load value can be calculated according to the formula (5) in this paper. At this time, Δlt in formula (6) needs to be replaced with Δl, and l is replaced with the original element length of the closure point. (5) After the length of the closure joint changes, the stress state of the structure has changed. At this time, the axial compression caused by the constant load, overall temperature change, and shrinkage does not change, but the axial compression caused by creep changes. Therefore, it is necessary to recalculate the creep internal force Mc and the total internal force Mi of the structure after the length of the closure joint changes over ten years. (6) If Mi / Mg < 0.1, the total internal force of the structure over ten years will be reduced by one order of magnitude compared with the original dead load internal force. If Mi / Mg > 0.1, repeat steps (3) to (6).

[0054] (7) Output the final closure length dx .

[0055] Specifically, the steps for bending moment amplitude adjustment using the influence matrix method include: Establish the arch crown bending moment after cable removal and arch construction Arch foot bending moment Length of the closure opening of the arch before the cable-stayed arch is dismantled With corner Relationship; ; For the influence matrix, These are the bending moments at the crown and abutments of the arch after the cables are removed and the arch is constructed; among which Represented as: ; These represent the arch crown bending moment values ​​after the cables are removed and the arch is formed by setting a unit horizontal displacement and rotation angle at the closure joint, respectively. These represent the arch foot bending moment values ​​after the cables are removed and the arch is formed by setting a unit horizontal displacement and rotation angle at the closure point, respectively. The coefficient matrix is ​​calculated using the finite element method. according to The coefficient matrix is ​​used to calculate the horizontal displacement dx and the rotation target ry at the closure point; .

[0056] Specifically, when the length of the closure joint changes, the total internal force M of the arch crown and arch foot of the structure must be recalculated. i and M j ; If M i / M g If the value is less than 0.1, output the closure length dx and the turning angle ry at this time.

[0057] In a specific embodiment of the present invention, the method for adjusting the bending moment amplitude based on the influence matrix of constant load and long-term effect includes: For large-span arch bridges where there is no analytical expression for the change in the cross-sectional area of ​​the arch ring, the compressive strain cannot be expressed analytically, and the axial compression is difficult to calculate accurately. The influence matrix method can be used for moment adjustment. According to equation (7), the bending moment of the arch rib under the reasonable arch axis is linearly related to the vertical coordinate of the arch axis, and its zero point is at... If the bending moments at the arch foot and arch crown can be made zero, then the bending moments at all points along the arch ribs can be guaranteed to be zero. Therefore, the arch crown bending moment after the cables are removed and the arch is formed can be established. Arch foot bending moment Length of the arch crown and the opening before the cable-stayed arch is dismantled With corner The relationship.

[0058] (7) (8) In equation (8), For the influence matrix, These are the horizontal displacement and rotation at the closure point, and the bending moments at the arch crown and arch foot after the cables are removed and the arch is formed. It can be expressed as equation (9).

[0059] (9) These represent the arch crown bending moment values ​​after the cables are disassembled and the arch is formed, with unit horizontal displacement and rotation angle set at the stern and ventral joints, respectively. These represent the arch foot bending moment values ​​after the cables are disassembled and the arch is formed, with unit horizontal displacement and rotation angle set at the stern and ventral joints, respectively. The coefficient matrix can be calculated using the finite element method, and the horizontal displacement and rotation target of the closure point can be solved according to equation (10).

[0060] (10)

[0061] Similarly, since the stress state of the structure changes after the closure section length changes, the internal forces caused by creep also change, thus requiring iterative calculations. The method for adjusting the bending moment amplitude based on the influence matrix of the dead load and long-term effects is as follows: Figure 4 As shown.

[0062] (1) Establish a spatial frame element model of the long-span arch bridge based on the design parameters; (2) Calculate the internal forces M of the arch ring, arch crown, and arch foot caused by dead load, shrinkage, and creep. c M s ; (3) Solve the coefficient matrix based on the finite element method. ; (4) Solve according to equation (8) dx ,ry; (5) The total internal force M of the arch crown and arch foot after recalculation and change of the arch mouth length. i M j ; (6) If M i / M g If M < 0.1, then the total internal force M at the top of the structure is... i Compared to the original dead load internal force M g Reducing it by one order of magnitude allows us to proceed to the next step (7). If M i / M c If the value is greater than 0.1, then the adjustment amount of the closure joint needs to be increased, specifically by setting M... c =M i M s =M j Complete the process and repeat steps (4) to (6).

[0063] (7) Output the final closure lengths dx and ry.

[0064] Specifically, when the horizontal displacement of the closure joint changes, the total internal force M of the arch crown and arch foot of the structure must be recalculated. i and M j ; If M i / M g <0.1 indicates that the internal forces of the completed bridge after adopting the active moment adjustment method for long-span arch bridges are less than one order of magnitude less than the capacity of a single bridge closure. Output the horizontal displacement of the current closure section. dx and corner target ry .

[0065] In another specific embodiment provided by the present invention, the live load bending moment adjustment method based on the influence matrix includes: The internal forces generated by moving loads cannot be completely eliminated by compensating for axial compression alone. One method for adjusting the internal forces of the arch ring under moving loads is to incorporate live loads with specific distribution patterns (e.g., full-span distribution) into the dead load considerations, achieving the offsetting of this portion of the bending by adjusting the arch axis and axial compression. This method only requires adjusting the load on the arch columns, but it significantly alters the structural stress state. If the arch bridge operates under other live load distribution patterns for an extended period, this method may adversely affect the structural stress. Another method is to adjust the length and rotation of the arch crown closure section to equalize the peak bending stress at each control section of the arch rib under a fixed distribution of moving loads. This method does not change the structural axis, thus causing less alteration to the structural stress state. The following section introduces this method using a full-span moving load as an example.

[0066] When the moving load is fully distributed across the entire span, the load value transmitted by the upper columns of the arch ring is approximately equal, and the bending distribution of the arch ring approximates that of a uniformly distributed load. This is because the arch axis used in long-span arch bridges has a quarter-point height... All these values ​​are higher than the parabola, therefore, under uniformly distributed load, the arch ring bending moment of a long-span arch bridge will pass through the zero moment point twice at half span, with positive bending moment peaks at the arch crown and arch foot, and negative bending moment peaks at L / 4. Figure 5 As shown. Similarly, stress peaks in the arch ring will appear at the crown, arch foot, and L / 4 position, as shown. Figure 6 As shown.

[0067] The principle of the live load bending moment adjustment method based on the influence matrix is: the target vector needs to be replaced by the difference between the bending moments at the arch crown and arch foot with the peak stress. After the cables are removed and the arch is formed, the bending stress at the arch crown is... The arch foot bending stress is The bending stress at L / 4 is This requires considering the length of the arch and the dragon's mouth. With corner The adjusted stresses are respectively , The relative change in bending stress at the crown and L / 4 point after the cables are removed and the arch is formed can be established. The relative change in bending stress at the arch foot and L / 4 Length of the arch crown and the opening before the cable-stayed arch is dismantled With corner The relationship.

[0068] (11)

[0069] In equation (11), The influence matrix can be expressed as equation (12). These represent the arch crown bending moment values ​​after the cables are disassembled and the arch is formed, with unit horizontal displacement and rotation angle set at the stern and ventral joints, respectively. These represent the arch foot bending moment values ​​after the cables are disassembled and the arch is formed, with unit horizontal displacement and rotation angle set at the stern and ventral joints, respectively. The coefficient matrix can be calculated using the finite element method, and the horizontal displacement and rotation target at the closure point can be solved according to equation (13). The live load bending moment adjustment method based on the influence matrix has a simple process and will not be described in detail here.

[0070] (12) (13) In a specific embodiment of the present invention, the process of solving the cable force during construction includes: When the length of the closure joint dx and corner ry Once determined, the cable forces during construction must be calculated. T i Using the aforementioned spatial frame element model of the long-span arch bridge, the cable forces during construction were calculated. T i Relative closure length dx and corner ry Influence Matrix D In the formula: T i Indicates the first i The initial tension of the horn cable.

[0071]

[0072] Since the number of cable forces during construction will inevitably exceed 2, the constraints imposed by the two objectives of closure length and turning angle on the cable forces during construction are insufficient. To further solve this problem, multiple optimization objectives can be introduced simultaneously, such as the uniformity of cable forces during construction and tower deflection during construction. This transforms the rankless matrix optimization problem into a linear equation problem, allowing the cable forces during construction to be obtained.

[0073] In a specific embodiment of the present invention, the verification process of the bending moment amplitude adjustment method includes: To verify the effectiveness of the moment adjustment method proposed in this embodiment for arch bridges with different spans, finite element method was used for calculation and analysis. Figure 7 This section compares the dead load bending moments of arch bridges with different spans after a single erection and after adjustment. Figure 7 It can be seen that after axial compression compensation at the closure joint, the dead load bending moment of the arch rib is significantly reduced. Figure 7 (b) For the 600m arch bridge, after adopting the internal force adjustment method, the bending moment at the top of the arch decreased to 0.3% of the original bending moment value, the bending moment at the foot of the arch decreased to 0.1% of the original bending moment value, and the bending moment value of the arch rib decreased by 2-3 orders of magnitude. The internal force adjustment method proposed in this embodiment can effectively improve the dead load bending moment of the long-span arch bridge.

[0074] To further verify the effectiveness of the moment adjustment method in this embodiment for adjusting the long-term bending effect, a calculation analysis is conducted using a long-span arch bridge. Example span It is 420m, with a rise of 420m. The column spacing is 70m. It is 31m long, and the vaulted ceiling has no columns. See Figure 8 .

[0075] Figure 9 The calculation results are for a 420m span example, where Figure 9 (a) The result of adjusting the dead load internal forces of the arch in the example. Figure 9 (b) shows the adjustment results of constant load + contraction internal force.

[0076] Depend on Figure 9 (a) It can be seen that after one set-up, the bending moments at the arch crown and arch foot are 3.2 × 10⁴ kN × m and -8 × 10⁴ kN × m, respectively. This can be addressed by increasing the length of the arch crown and the arch opening. dx After the diameter reaches 82.9 mm, the bending moment range of the arch rib is -75 to 49 kN×m, at which point the arch rib is essentially under pure compression. Figure 9 (b) It can be seen that the dead load of the one-time formed structure plus the internal force of the shrinkage arch foot is -1.2×105kN×m. By increasing the length of the arch crown and the spur opening... dx After the amplitude is adjusted to 120.2 mm, the internal force is -3.7 × 10³ kN × m, which is only 3.8% of the original internal force value.

[0077] Furthermore, by iteratively calculating and adjusting the internal force effects caused by creep at the closure point... dx When the diameter is 1141.5mm, the total bending moment of the structure is adjusted to a smaller value. The bending moments of each component of the arch rib under different closure joint lengths are plotted on [the graph]. Figure 10 ,in Figure 10 (a), (b), (c), and (d) represent the dead load, shrinkage, creep, and total structural bending moment, respectively. The dead load bending moment includes the bending moment effect generated by the structural dead load and the growth of the arch and the opening. The total structural bending moment is the sum of the dead load, shrinkage, and creep. dx =0, 82.9, 120.2 and 1141.5 correspond to the adjustment of bending moment under first-time frame removal, structural dead load, dead load + shrinkage bending moment, and total structural bending moment, respectively.

[0078] Depend on Figure 10 (a) It can be seen that after one dismantling... dx =0, the dead load bending moment is positive at the arch crown and negative at the arch foot. By setting different opening lengths, the structure can store a reverse bending moment to counteract the internal forces generated by subsequent shrinkage and creep; the longer the opening, the greater the value of the reverse bending moment stored in the structure. Figure 10(b) shows that after changing the length of the opening, the bending moment generated by the structural contraction remains unchanged, and its distribution is consistent with the dead load bending moment during the first frame lowering, with a value approximately half that of the dead load bending moment. Figure 10 (c) It can be seen that the creep moment of the structure is opposite in direction to the dead load moment. Creep causes a redistribution of internal forces, leading to the development of the total internal forces of the structure in the direction of the first frame drop. When the preset dead load reverse moment value is larger, the creep-generated moment value is also larger, but the increase in creep moment is less than the preset increase in dead load reverse moment. Therefore, the creep moment value can eventually be completely canceled out, but the required preset dead load reverse moment value is relatively large. Figure 10 (d) It can be seen that in dx When the creep moment is 82.9 mm and 120.2 mm, although the preset dead load reverse bending moment values ​​can offset the dead load bending moment and the dead load + shrinkage bending moment of the arch rib structure respectively, the actual total bending moment of the structure is similar to the bending moment value during the first frame lowering due to the increase in creep moment value. dx When the creep length is 82.9, 120.2, and 1141.5 mm, the total bending moment of the arch rib decreases by 6.9%, 10.1%, and 95.6%, respectively. Although the creep effect is partially linear, the decrease in the total bending moment of the arch rib is strictly linearly correlated with the increase in the length of the arch opening.

[0079] Existing long-span arch bridges experience a gradual increase in bending moments within the arch ring under the influence of dead load and shrinkage / creep, leading to a deterioration in the arch ring's stress state. This embodiment of the method adjusts the internal forces within the arch ring by preemptively applying the effects of dead load, shrinkage, and creep bending moments in reverse to the structure. This brings the most unfavorable structural condition to the maximum double cantilever state. As the dead load is applied (due to cable removal and arch closure) and the shrinkage and creep effects act on the structure, this preemptively applied reverse bending moment is gradually offset, transforming the process of internal force change within the arch ring from deterioration to optimization. This results in a better stress state for the arch ring during long-term use, ultimately achieving the goal of bending moment adjustment.

[0080] It should be emphasized that this embodiment is well applicable to steel arch bridges with minimal creep, but for concrete arch bridges with significant creep, the internal forces in the arch ring caused by creep shrinkage are difficult to offset, and the closure length in this example needs to be increased. dx A 95.6% reduction in the total bending moment of the arch rib is achieved only when the diameter reaches 1141.5 mm. However, at this point, the bending stress in the maximum double cantilever state of the arch rib reaches 46.9 MPa, and the compressive stress level of the arch rib is 16 MPa, indicating that the concrete has already cracked. If a compressive stress reserve of at least 1 MPa is controlled, the allowable bending stress in the maximum double cantilever state is 15 MPa, at which point... dx =413.9mm, corresponding to a total bending moment reduction of 33.4%.

[0081] To verify the effectiveness of the moment adjustment method proposed in this embodiment for adjusting live load bending stress, finite element analysis was performed, and for example, [the following was conducted]. Figure 11 As shown. Figure 11 The comparison results of live load bending stress and bending moment of the arch bridge after the first erection and after the amplitude adjustment are shown in the example. Figure 11 (a) shows the calculation results of bending stress. Figure 11 (b) shows the bending moment calculation results.

[0082] Depend on Figure 3 As shown in .41(a), after axial compression compensation at the closure joint, the distribution of bending stress generated by the live load of the arch rib did not change significantly, but the overall value shifted towards negative bending moment. The stresses at the arch foot, L / 4, and arch crown changed from 1.42MPa, -0.86MPa, and 1.08MPa to 1.07MPa, -1.07MPa, and 1.07MPa, respectively. The distribution of bending stress in the arch rib became more uniform. The internal force adjustment method proposed in this paper can effectively improve the live load stress of long-span arch bridges.

[0083] Depend on Figure 11 (b) It can be seen that the change in bending moment of the arch rib is basically consistent with the change in bending stress. The peak bending moment of the arch crown and arch foot can be adjusted by changing the length of the arch crown and arch opening, so that the larger value decreases and the smaller value increases. In this embodiment, the stress of the arch foot and arch crown before adjustment is 1.42MPa and 1.07MPa, respectively. Therefore, the negative bending moment of the arch foot and the positive bending moment of the arch crown can be generated by increasing the length of the arch crown and arch opening, so that the two values ​​are close. The length of the arch crown and arch opening and the angle together can change the overall value of the bending moment. The change of the arch opening angle will produce an axial compression bending moment effect and a fixed bending moment effect distributed throughout the span. The axial compression bending moment effect and the bending moment effect produced by increasing the length of the arch crown and arch opening are consistent and can cancel each other out. Therefore, the two can jointly control the overall value of the bending moment.

[0084] To further verify the feasibility of the moment adjustment method proposed in this paper in the construction of arch bridges, finite element method was used for calculation and analysis. Figure 12 The 420m arch bridge case mentioned in this embodiment ( Figure 8 Considering the finite element model for the construction phase, the simulation model uses variable cross-section beam elements to simulate the main arch, totaling 875 beam elements, and truss elements to simulate the cable ties, totaling 36 truss elements. The truss elements and beam elements are connected by common nodes. The simulation model uses fixed boundary conditions at the arch feet on both sides and the ends of the cable ties. The construction phases of the model are divided into the maximum cantilever condition, the closure condition, and the cable ties removal and arch formation condition.

[0085] In this embodiment, the cable force calculation employs the influence matrix method, solving for the cable force by setting the horizontal displacement dx and angular displacement ry at the closure point as target values. In this embodiment, it is necessary to increase the length of the arch and the closure point during the maximum cantilever stage. dx =82.9mm, and with the angular displacement ry=0 at the duct opening, the bending moment adjustment under dead load can be guaranteed. The cable force can then be obtained. Figure 13 The calculation results for the cable-to-arch construction condition after cable force calculation using this method are shown below. Figure 13 (a), (b), and (c) show the calculated results of the arch rib deflection, bending moment, and stress after the cables were removed and the arch was constructed. Figure 13 (a) shows that after the cables are removed and the arch is formed, the deflection of the arch rib changes linearly with the height loss, indicating that the deformation of the arch rib at this time is only caused by compressive deformation and not bending deformation. Figure 13 (b) It can be seen that the maximum bending moment after adjusting the internal forces using the tie cable occurs at the arch crown at -71 kN×m, while the maximum bending moment after the first arch formation occurs at the arch foot at -80.2×10³ kN×m. The bending moment after adjusting the internal forces using the tie cable is reduced by three orders of magnitude compared to the bending moment after the first arch formation. Figure 13 (c) It can be seen that the axial compressive stress of the arch after internal force adjustment by using the buckle is a constant value of 15MPa, while the bending stress is a small value close to 0 throughout the entire arch rib range.

[0086] In summary, to reduce this bending moment, this invention proposes a bending moment adjustment method based on axial compression compensation. By increasing the length of the maximum cantilever stage and the gap between the arch ribs, the completed long-span arch bridge can approach a state of pure compression. A case study analysis was conducted on a 420m span arch bridge. After applying the bending moment adjustment method, the dead load bending moment value of the arch rib can be reduced by 2-3 orders of magnitude. Considering long-term effects, the total structural bending moment reduction is 34.4%, and the bending stress generated by live load is reduced by 24.6%.

[0087] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0088] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for active moment adjustment of long-span arch bridges based on cable forces during construction, characterized in that, include: Establish a spatial frame unit model of the long-span arch bridge based on the design parameters; Calculate the internal forces at the crown of the arch ring based on the spatial frame element model of a long-span arch bridge; Calculate the corresponding change in compression based on the internal forces at the top of the arch ring; The final amplitude modulation closure length is obtained based on the change in compression. The cable force of the long-span arch bridge is calculated based on the length of the closure gap, thereby realizing the adjustment of the internal force of the completed long-span arch bridge.

2. The active moment adjustment method for long-span arch bridges based on cable forces during construction, as described in claim 1, is characterized in that... The design parameters include the span, rise, column spacing, material properties, and cross-sectional shape of the long-span arch bridge; the spatial truss unit model of the long-span arch bridge uses variable cross-section beam units to simulate the main arch, truss units to simulate the cable tie, beam units and truss units are connected at common nodes, and fixed boundary conditions are set at the arch foot and cable tie ends.

3. The active moment adjustment method for long-span arch bridges based on cable forces during construction, as described in claim 2, is characterized in that... The internal forces at the crown of the arch include Ms , Mg and Mc , Ms , Mg, Mc These represent the internal force values ​​for dead load, shrinkage, and creep calculated using the finite element method, with the values ​​taken from the crown of the arch for calculation.

4. The active moment adjustment method for long-span arch bridges based on cable forces during construction, as described in claim 3, is characterized in that... The process of calculating the corresponding compression change value based on the internal force of the arch ring and crown includes: compressive strain caused by constant load change, compressive strain caused by temperature change, compressive strain caused by shrinkage change, and compressive strain caused by creep. The compressive strain induced by dead load yields different expressions for dead load strain depending on the cross-sectional shape. ； Integrating the above equation, we obtain the expression for constant load compressive strain. ； in, Represents the compressive strain function under constant load. This represents the compression function of the arch rib under constant load. This represents the compressive strain value of the arch crown. a Indicates the curvature of the vault. l It represents half the arch span. A x This is a function representing the variation of the arch rib cross section. A 0 represents the cross-sectional area of ​​the arch crown. Indicates the horizontal inclination angle of the arch axis; The compressive strain caused by temperature change is expressed as ; in, This is the difference between the temperature at the time of closure and the average temperature. The coefficient of thermal expansion of the material. l It is represented as half the arch span. The compressive strain caused by contraction is calculated using the finite element method, as shown in the following formula: ； The compressive strain caused by creep is calculated based on the ratio of shrinkage to the bending moment of the dead load arch rib, using the following formula: 。 5. The active moment adjustment method for long-span arch bridges based on cable forces during construction, as described in claim 4, is characterized in that... The final expression for the amplitude modulation closure gap length is as follows: dx =D lg +D lt +D ls +D lc。 6. The active moment adjustment method for long-span arch bridges based on cable forces during construction, as described in claim 5, is characterized in that... When the amplitude modulation closure length dx After the changes, the stress state of the structure has changed. At this time, the axial compression caused by dead load, overall temperature change, and shrinkage remains unchanged, while the axial compression caused by creep changes. Therefore, it is necessary to recalculate the ten-year creep internal forces of the structure after the change in the length of the gap. M c With total internal force M i ; when M i / M g When <0.1, output the amplitude modulation closure gap length value at this time. dx .

7. The method for active moment adjustment of a long-span arch bridge based on cable forces during construction, as described in claim 1, is characterized in that... It also includes the use of the influence matrix method for bending moment adjustment when there is no analytical expression for the cross-sectional area of ​​the compressive strain caused by the constant load, in which case the change in compression cannot be accurately calculated analytically.

8. The active moment adjustment method for long-span arch bridges based on cable forces during construction, as described in claim 7, is characterized in that... The specific steps for bending moment amplitude adjustment using the influence matrix method include: Establish the arch crown bending moment after cable removal and arch construction Arch foot bending moment Length of the closure opening of the arch before the cable-stayed arch is dismantled With corner Relationship; ； For the influence matrix, These are the bending moments at the crown and abutments of the arch after the cables are removed and the arch is constructed; among which Represented as: ； These represent the arch crown bending moment values ​​after the cables are removed and the arch is formed by setting a unit horizontal displacement and rotation angle at the closure joint, respectively. These represent the arch foot bending moment values ​​after the cables are removed and the arch is formed by setting a unit horizontal displacement and rotation angle at the closure point, respectively. The coefficient matrix is ​​calculated using the finite element method. according to The coefficient matrix is ​​used to calculate the horizontal displacement dx and the rotation target ry at the closure point; 。 9. The method for active moment adjustment of a long-span arch bridge based on cable forces during construction, as described in claim 7, is characterized in that... When the horizontal displacement of the closure joint changes, the total internal forces at the arch crown and arch foot of the structure must be recalculated. M i and M j ; like M i / M g <0.1 indicates that the internal forces of the completed bridge after adopting the active moment adjustment method for long-span arch bridges are less than one order of magnitude less than the capacity of a single bridge closure. Output the horizontal displacement of the current closure section. dx and corner target ry .

10. The method for active moment adjustment of a long-span arch bridge based on cable forces during construction, as described in claim 9, is characterized in that... When the horizontal displacement of the closure joint dx and corner ry Once determined, the cable forces during construction must be calculated. T i ; Using the aforementioned spatial frame element model of the long-span arch bridge, the cable forces during construction were calculated. T i Horizontal displacement relative to the closure point dx and corner target ry Influence Matrix D In the formula: T i Indicates the first i The initial tension of the horn cable; Since the number of cable forces during construction must exceed 2, the two objectives of horizontal displacement and rotation at the closure point are insufficient to constrain the cable forces during construction. To further solve the problem, multiple optimization objectives such as cable force uniformity during construction and tower deflection during construction are introduced. The rankless matrix optimization problem is transformed into a linear equation problem, and the cable forces during construction are obtained by solving the problem.

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